S. Kanade

activity

20142026

most citedTensor categories for vertex operator superalgebra extensions

92 citations · 389 across the 26 of their papers we have counts for

collaborators

28 papers

math.QA2026

Classical freeness of $sl_{n}$ at level $1$ via combinatorics

Shashank Kanade

We use a family of Rogers--Ramanujan-type combinatorial identities of Dousse--Konan involving coloured partitions to prove classical freeness of the simple vertex operator algebras…

math.CO2025

Tight cylindric partitions

Shashank Kanade, Matthew C. Russell

In this note, we initiate the study of generating functions for tight cylindric partitions. For general (i.e., $r$ -rowed for $r \geq 2$ ) tight cylindric partitions, we provide analo…

math.CA2024

Bailey Pairs and an Identity of Chern-Li-Stanton-Xue-Yee

Shashank Kanade, Jeremy Lovejoy

We show how Bailey pairs can be used to give a simple proof of an identity of Chern, Li, Stanton, Xue, and Yee. The same method yields a number of related identities as well as fal…

math.CO2024

Remarks on the conjectures of Capparelli, Meurman, Primc and Primc

Shashank Kanade, Matthew C. Russell, Shunsuke Tsuchioka +1

In a series of two papers, S. Capparelli, A. Meurman, A. Primc, M. Primc (CMPP) and then M. Primc put forth three remarkable sets of conjectures, stating that the generating functi…

math.QA2024

Coloured invariants of torus knots, $W$ algebras, and relative asymptotic weight multiplicities

Shashank Kanade

We study coloured invariants of torus knots $T (p, p^{'})$ (where $p, p^{'}$ are coprime positive integers). When the colouring Lie algebra is simply-laced, and when $p, p^{'} \geq h^{\lor}$ , we u…

math.QA2023

Characters of logarithmic vertex operator algebras and coloured invariants of torus links

Shashank Kanade

We show that the characters of $sl_{r}$ versions of the $(1, p)$ singlet and the $(1, p)$ triplet VOAs arise as limits of appropriately coloured $sl_{r}$ Jones inva…

math.CO2022

Principal subspaces of basic modules for twisted affine Lie algebras, $q$ -series multisums, and Nandi's identities

Katherine Baker, Shashank Kanade, Matthew C. Russell +1

We provide an observation relating several known and conjectured $q$ -series identities to the theory of principal subspaces of basic modules for twisted affine Lie algebras. We als…

math.QA2022★ 3 cited

Coloured $sl_{r}$ invariants of torus knots and characters of $W_{r}$ algebras

Shashank Kanade

Let $p < p^{'}$ be a pair of coprime positive integers. In this note, generalizing Morton's work in the case of $sl_{2}$ , we give a formula for the $sl_{r}$ Jones inva…

math.CO2022★ 2 cited

Completing the $A_{2}$ Andrews-Schilling-Warnaar identities

Shashank Kanade, Matthew C. Russell

We study the Andrews-Schilling-Warnaar sum-sides for the principal characters of standard (i.e., integrable, highest weight) modules of $A_{2}^{(1)}$ . These characters have…

math.NT2021

On certain identities involving Nahm-type sums with double poles

Shashank Kanade, Antun Milas, Matthew C. Russell

We prove certain Nahm-type sum representations for the (odd modulus) Andrews-Gordon identities, the (even modulus) Andrews-Bressoud identities, and Rogers' false theta functions. T…

math.RT2020

On $q$ -series for principal characters of standard $A_{2}^{(2)}$ -modules

Shashank Kanade, Matthew C. Russell

We present sum-sides for principal characters of all standard (i.e., integrable and highest-weight) irreducible modules for the affine Lie algebra $A_{2}^{(2)}$ . We use modifications…

math.QA2020

$A_{2 l}^{(2)}$ at level $- l - \frac{1}{2}$

Shashank Kanade

Let $L_{l} = L (sl_{2 l + 1}, - l - \frac{1}{2})$ be the simple vertex operator algebra based on the affine Lie algebra $sl_{2 l + 1}$ at boundary admissible lev…

math.QA2019★ 26 cited

Braided Tensor Categories related to $B_{p}$ Vertex Algebras

Jean Auger, Thomas Creutzig, Shashank Kanade +1

The $B_{p}$ -algebras are a family of vertex operator algebras parameterized by $p \in Z_{\geq 2}$ . They are important examples of logarithmic CFTs and appear as chir…

math.QA2019★ 31 cited

Gluing vertex algebras

Thomas Creutzig, Shashank Kanade, Robert McRae

We relate commutative algebras in braided tensor categories to braid-reversed tensor equivalences, motivated by vertex algebra representation theory. First, for $C$ a bra…

math.NT2019

Searching for modular companions

Shashank Kanade

In this note, we report on the results of a computer search performed to find possible modular companions to certain $q$ -series identities and conjectures. For the search, we use c…

math.CO2019★ 1 cited

A variant of $IdentityFinder$ and some new identities of Rogers-Ramanujan-MacMahon type

Shashank Kanade, Debajyoti Nandi, Matthew C. Russell

We report on findings of a variant of $IdentityFinder$ - a Maple program that was used by two of the authors to conjecture several new identities of Rogers-Ramanujan kin…

math-ph2018

NGK and HLZ: fusion for physicists and mathematicians

Shashank Kanade, David Ridout

In this expository note, we compare the fusion product of conformal field theory, as defined by Gaberdiel and used in the Nahm-Gaberdiel-Kausch (NGK) algorithm, with the $P (w)$ -ten…

hep-th2018★ 30 cited

Cosets, characters and fusion for admissible-level $osp (1∣2)$ minimal models

Thomas Creutzig, Shashank Kanade, Tianshu Liu +1

We study the minimal models associated to $osp (1∣2)$ , otherwise known as the fractional-level Wess-Zumino-Witten models of $osp (1∣2)$ . Since these…

math.RT2018★ 24 cited

Universal two-parameter even spin $W_{\infty}$ -algebra

Shashank Kanade, Andrew R. Linshaw

We construct the unique two-parameter vertex algebra which is freely generated of type $W (2, 4, 6, \dots)$ , and generated by the weights $2$ and $4$ fields. Subject to some…

math.CO2018

Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type

Shashank Kanade, Matthew C. Russell

We utilize the technique of staircases and jagged partitions to provide analytic sum-sides to some old and new partition identities of Rogers-Ramanujan type. Firstly, we conjecture…

math.QA2017★ 5 cited

Representation theory of $L_{k} (osp (1∣2))$ from vertex tensor categories and Jacobi forms

Thomas Creutzig, Jesse Frohlich, Shashank Kanade

The purpose of this work is to illustrate in a family of interesting examples how to study the representation theory of vertex operator superalgebras by combining the theory of ver…

math.QA2017★ 92 cited

Tensor categories for vertex operator superalgebra extensions

Thomas Creutzig, Shashank Kanade, Robert McRae

Let $V$ be a vertex operator algebra with a category $C$ of (generalized) modules that has vertex tensor category structure, and thus braided tensor category structure, a…

math.CO2017

On a dual and an overpartition generalization of a family of identities of Andrews

Shashank Kanade, Matthew C. Russell

We present a dual of a family of partition identities of Andrews involving partitions with no repeated odd parts (among other conditions), along with an overpartition generalizatio…

math.QA2016★ 86 cited

Schur-Weyl Duality for Heisenberg Cosets

Thomas Creutzig, Shashank Kanade, Andrew R. Linshaw +1

Let $V$ be a simple vertex operator algebra containing a rank $n$ Heisenberg vertex algebra $H$ and let $C = Com (H, V)$ be the coset of $H$ in $V$ . Assumin…

Classical freeness of sln​ at level 1 via combinatorics

Tight cylindric partitions

Bailey Pairs and an Identity of Chern-Li-Stanton-Xue-Yee

Remarks on the conjectures of Capparelli, Meurman, Primc and Primc

Coloured invariants of torus knots, W algebras, and relative asymptotic weight multiplicities

Characters of logarithmic vertex operator algebras and coloured invariants of torus links

Principal subspaces of basic modules for twisted affine Lie algebras, q-series multisums, and Nandi's identities

Coloured slr​ invariants of torus knots and characters of Wr​ algebras

Completing the A2​ Andrews-Schilling-Warnaar identities

On certain identities involving Nahm-type sums with double poles

On q-series for principal characters of standard A2(2)​-modules

A2l(2)​ at level −l−21​

Braided Tensor Categories related to Bp​ Vertex Algebras

Gluing vertex algebras

Searching for modular companions

A variant of IdentityFinder and some new identities of Rogers-Ramanujan-MacMahon type

NGK and HLZ: fusion for physicists and mathematicians

Cosets, characters and fusion for admissible-level osp(1∣2) minimal models

Universal two-parameter even spin W∞​-algebra

Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type

Representation theory of Lk​(osp(1∣2)) from vertex tensor categories and Jacobi forms

Tensor categories for vertex operator superalgebra extensions

On a dual and an overpartition generalization of a family of identities of Andrews

Schur-Weyl Duality for Heisenberg Cosets

Classical freeness of $sl_{n}$ at level $1$ via combinatorics

Coloured invariants of torus knots, $W$ algebras, and relative asymptotic weight multiplicities

Principal subspaces of basic modules for twisted affine Lie algebras, $q$ -series multisums, and Nandi's identities

Coloured $sl_{r}$ invariants of torus knots and characters of $W_{r}$ algebras

Completing the $A_{2}$ Andrews-Schilling-Warnaar identities

On $q$ -series for principal characters of standard $A_{2}^{(2)}$ -modules

$A_{2 l}^{(2)}$ at level $- l - \frac{1}{2}$

Braided Tensor Categories related to $B_{p}$ Vertex Algebras

A variant of $IdentityFinder$ and some new identities of Rogers-Ramanujan-MacMahon type

Cosets, characters and fusion for admissible-level $osp (1∣2)$ minimal models

Universal two-parameter even spin $W_{\infty}$ -algebra

Representation theory of $L_{k} (osp (1∣2))$ from vertex tensor categories and Jacobi forms